Single-site dissipation stabilizes a superconducting nonequilibrium steady state in a strongly correlated system

TL;DR

This paper demonstrates that a single-site dissipation protocol can stabilize a superconducting nonequilibrium steady state with long-range order in a strongly correlated Hubbard model, offering a robust, disorder-tolerant method for engineering superconductivity.

Contribution

It introduces a minimal local dissipation scheme using a rotated quantum jump operator to stabilize superconducting order as a non-thermal attractor in a strongly correlated system.

Findings

A single local dissipative seed induces long-range $ ext{eta}$-pairing order.

The stabilized NESS is robust against static disorder and certain Hamiltonian perturbations.

The mechanism involves local dark-state selection and invariant subspace structure.

Abstract

Can superconducting order be engineered as a robust attractor of open-system dynamics in strongly correlated systems? We demonstrate this possibility by proposing a minimal dissipation-engineering protocol for the particle-hole symmetric Hubbard model. By applying a rotated quantum jump operator, specifically a locally transformed $\eta$-pair lowering operator, on a single lattice site only, we show that the Lindblad evolution autonomously pumps the system from the vacuum into a nonequilibrium steady state (NESS) exhibiting macroscopic $\eta$-pair off-diagonal long-range order (ODLRO). Crucially, this local-to-global synchronization stands in stark contrast to schemes reliant on spatially extensive reservoirs: here, a single local dissipative seed suffices to establish long-range coherence across the entire interacting lattice system. We elucidate the underlying mechanism via three core features: local dark-state selection, the controlled elimination of off-manifold excursions induced by hopping, and a Liouvillian invariant-subspace structure that yields an attractive fixed point with a finite dissipative gap. Furthermore, we systematically classify the stability of this NESS with respect to static disorder, and identify a wide regime in which the superconducting attractor remains robust against Hamiltonian perturbations that preserve the effective subspace structure. We also pinpoint specific perturbations that directly cause dephasing of the $% \eta$-pseudospin coherence and suppress ODLRO. These findings open up a disorder-tolerant pathway for stabilizing superconducting order as a non-thermal attractor through minimal local quantum-jump control.